One important type of automotive blind-spot or pre-crash warning system employs short pulses of electromagnetic or ultrasonic energy to interrogate the detection zone. A decision regarding the presence or absence of an obstacle at a predetermined range is then made by suitably processing energy backscattered by various objects in the field of view of the system. A detection apparatus can be arranged to detect whether a reflected pulse appears at a particular delay (corresponding to the predetermined range) after the interrogation pulse has been transmitted. Instead of just detecting the occurrence of reflected pulses, the analog values of the signal received after each pulse transmission can be integrated, to provide an arrangement which is sensitive to backscattered signal strength, and thus capable of better performance. A multichannel detection apparatus has several channels, each with a different delay, for detecting objects at different range values of interest.
It is known that object detectability can be improved significantly when each single pulse is replaced by a suitably-constructed pulse packet. Each pulse packet comprises a specified number N of identical pulses which are staggered nonuniformly, with each interpulse spacing being an integer multiple of a suitably chosen unit time interval. The pattern of interpulse spacings is so designed as to ensure that only a small number ha of pulse coincidences (preferably at most one pulse coincidence) will occur between a primary pulse packet and its replica shifted in time by more than one pulse duration. This condition is usually referred to as the autocorrelation constraint.
Consider a pulse packet of span (length) L comprising N identical rectangular pulses of unit duration. Such a pulse packet can be conveniently represented by a binary sequence {x}=x1 x2 . . . xL of symbols 0 and 1, in which symbol 1 corresponds to pulse occurrence. In this case, the autocorrelation constraint can be expressed as
                    R        xx            ⁡              (        d        )              =                            ∑                      i            =            1                                L            -            d                          ⁢                              x            i                    ⁢                      x                          i              +              d                                          ≤              h        a            <      N        ,          ⁢      0    <    d    ≤          L      -      1      where Rxx(d) is the autocorrelation sequence and d is the integer shift. When d=0, the autocorrelation value Rxx(0) simply equals the number N of pulses contained within the pulse packet.
In the class of all pulse packets with a specified number of pulses N and ha=1, a maximally compact pulse packet has the minimal span Lmin. Consequently, the maximally compact pulse packet exhibits the largest duty factor, N/L, hence the largest average power. For a fixed N and ha=1, all pulse packets with spans greater than Lmin are referred to as sparse pulse packets.
The autocorrelation constraint ensures that when there is no noise or interference, and a multichannel pulse-coincidence processor is used for detecting a pulse packet, the output of each channel is at most ha except when the channel delay matches that of a pulse packet being received. In this case, the channel output reaches the peak value of N.
In a multi-user environment, the users may transmit their signals simultaneously and asynchronously so that not only must each receiver recognize and detect its own transmitted signal, but it must be able to do so in the presence of the other transmitted signals. Assume that a pulse packet to be detected by a receiver of interest is represented by a binary sequence{x}=x1 x2 . . . xL and that one of the interfering pulse packets is represented by another binary sequence{y}=y1 y2 . . . yL 
In order to optimize the detection performance of the receiver in multi-user environment, the following cross-correlation constraints must be satisfied for all integer shifts d
                              R          xy                ⁡                  (          d          )                    =                                    ∑                          i              =              1                                      L              -              d                                ⁢                                    x              i                        ⁢                          y                              i                +                d                                                    ≤                  h          c                <        N              ,                  ⁢          0      ≤      d      ≤              L        -                  1          ⁢                                          ⁢          and                                                  R          yx                ⁡                  (          d          )                    =                                    ∑                          i              =              1                                      L              -              d                                ⁢                                    y              i                        ⁢                          x                              i                +                d                                                    ≤                  h          c                <        N              ,                  ⁢          0      ≤      d      ≤              L        -        1            
When more than one transmitter is in operation, the autocorrelation and cross-correlation constraints combined together ensure that when there is no noise and a multichannel pulse-coincidence processor is used for detection, the output of each channel is still substantially less than N except when the channel delay matches that of a received pulse packet of interest.
In automotive applications, many similar obstacle-detection systems should be capable of operating in the same region, and sharing the same frequency band. To avoid mutual interference, each system should use a distinct signal, preferably uncorrelated with the signals employed by all other systems. Because it is not possible to predict which of the many similar systems will be operating in a particular environment, it is not practical to assign a distinct binary sequence to each of them. Furthermore, it is also very difficult to construct large sets of binary sequences with good autocorrelation and cross-correlation properties, and also exhibiting acceptable duty factors.
European Patent Application No. EP-A-1330031 (referred to herein as “the earlier application”, and the contents of which are incorporated herein by reference) discloses a method which exploits random mechanisms to generate large sets of composite pulse trains that can satisfy both autocorrelation and cross-correlation constraints. Consequently, resulting composite pulse trains will exhibit an excellent resistance to mutual jamming in multi-user environments. It is also possible to produce sequences exhibiting a high duty factor, thus enhancing the resulting detection performance.
According to the method disclosed in the earlier application, a composite pulse train consists of a sequence of primary pulse packets each of which is drawn at random from a predetermined set of suitably constructed primary pulse packets with prescribed autocorrelation and cross-correlation properties. The autocorrelation function of each primary pulse packet exhibits the property of ‘at most one coincidence’. Also, the cross-correlation function between any two different pulse packets assumes small values compared to the maximum value of the corresponding autocorrelation functions. Furthermore, the resistance to mutual jamming in multi-user environments can be further improved by separating individual primary pulse packets by gaps of random duration, the value of which may be determined by a random value supplied by a random number generator. FIG. 1 depicts the structure of such constructed composite pulse trains.
As a result, although each user may have the same set of primary pulse packets, a composite pulse train transmitted by each user is assembled in a random manner and is, therefore, statistically unique.
Although the method disclosed in the earlier application offers a practical solution to the problem of alleviating the mutual interference effects in a multi-user environment, the method is not capable of increasing the ratio R of the peak autocorrelation value, Rxx(0)=N, to the maximum (unit) autocorrelation sidelobe value. Increasing the value of R would improve the capability of the obstacle-detection system to detect and discriminate smaller obstacles (such as motorbikes) located in proximity of larger obstacles (such as trucks).
It would therefore be desirable to provide a method for generating a large number of pulse trains with good autocorrelation properties, good cross-correlation properties, and also improved capability to discriminate between multiple smaller and larger obstacles, especially for applications in systems intended to operate in a multi-user environment.